Related papers: Generalization in quasi-periodic environments
We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in…
Imitation Learning (IL) has proven highly effective for robotic and control tasks where manually designing reward functions or explicit controllers is infeasible. However, standard IL methods implicitly assume that the environment dynamics…
The rapid progress in machine learning in recent years has been based on a highly productive connection to gradient-based optimization. Further progress hinges in part on a shift in focus from pattern recognition to decision-making and…
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
The algorithms used to train neural networks, like stochastic gradient descent (SGD), have close parallels to natural processes that navigate a high-dimensional parameter space -- for example protein folding or evolution. Our study uses a…
We investigate the detailed dynamics of multidimensional Hamiltonian systems by studying the evolution of volume elements formed by unit deviation vectors about their orbits. The behavior of these volumes is strongly influenced by the…
For the non-conservative Caldirola-Kanai system, describing a quantum damped harmonic oscillator, a couple of constant-of-motion operators generating the Heisenberg-Weyl algebra can be found. The inclusion of the standard time evolution…
We formulate a general method for the study of semiclassical-like dynamics in stable regions of a mixed phase-space, in order to theoretically study the dynamics of quantum accelerator modes. In the simplest case, this involves determining…
The notion of the stationary equilibrium ensemble has played a central role in statistical mechanics. In machine learning as well, training serves as generalized equilibration that drives the probability distribution of model parameters…
Learning the underlying potential energy of stochastic gradient systems from partial and noisy observations is a fundamental problem arising in physics, chemistry, and data-driven modeling. Classical approaches often rely on direct…
Stochastic gradient methods enable learning probabilistic models from large amounts of data. While large step-sizes (learning rates) have shown to be best for least-squares (e.g., Gaussian noise) once combined with parameter averaging,…
Among the most relevant processes in the Earth system for human habitability are quasi-periodic, ocean-driven multi-year events whose dynamics are currently incompletely characterized by physical models, and hence poorly predictable. This…
This paper proposes a data-driven learning framework for identifying governing laws of generalized diffusions with non-gradient components. By combining energy dissipation laws with a physically consistent penalty and first-moment…
Dissipative backflow is studied in the context of open quantum systems. This theoretical analysis is carried out within two frameworks, the effective time-dependent Hamiltonian due to Caldirola-Kanai (CK) and the Caldeira-Leggett (CL) one…
Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has become increasingly popular for simulating posterior samples in large-scale Bayesian modeling. However, existing SG-MCMC schemes are not tailored to any specific probabilistic…
Hybrid quantum-classical optimization algorithms represent one of the most promising application for near-term quantum computers. In these algorithms the goal is to optimize an observable quantity with respect to some classical parameters,…
Machine learning is a powerful method of extracting meaning from data; unfortunately, current digital hardware is extremely energy-intensive. There is interest in an alternative analog computing implementation that could match the…
Understanding and characterising quantum many-body dynamics remains a significant challenge due to both the exponential complexity required to represent quantum many-body Hamiltonians, and the need to accurately track states in time under…
In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Klein-Gordon equations in one space dimension. We classify the systems by studying the quotient set of a suitable subset of systems…
Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore…